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Calculus I Quiz
#4 February
24, 2004

Name____________________ R. Hammack Score
______

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(1)

(a)

(b)

(c)

(2) Find the domain of the function

First, x can't be negative, for that
would involve the square root of a negative number.

Second, x can't be such that 1+2cos(x)
= 0, for that would result in division by zero.

The equation 1+2cos(x) = 0 reduces
to cos(x) = -1/2,

so we are looking out for values of x
that make cos(x) = -1/2.

Looking at the unit circle, you can see that and
make
cos(x) = -1/2.

Of course, you could add any multiple of
to these values, and still cos(x) =
-1/2,

making the denominator in f(x)
zero.

Conclusion: The domain is

(3) In this problem,
is a number between 0 and
for which .

This information says ,

so it follows that . From
this it follows that ,
so .

Then:

(a)

(b)